A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions

Published in: Journal of Classification, vol. 25, no. 1, June 2008, p. [113]-123

Posted on RAND.org on December 31, 2007

by Erik Meijer, Jelmer Yeb Ypma

A simple proof of the identification of a mixture of two univariate normal distributions is given. The proof is based on the equivalence of local identification with positive definiteness of the information matrix and the equivalence of the latter to a condition on the score vector that is easily checked for this model. Two extensions using the same line of proof are also given.

This report is part of the RAND Corporation external publication series. Many RAND studies are published in peer-reviewed scholarly journals, as chapters in commercial books, or as documents published by other organizations.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.